2. Find contrast characteristics among the correlation coefficients above
contrast_helper <- function(contrast_ind, threshold){
to_track <- data.frame()
if (nrow(contrast_ind) == 0){
return (contrast_ind)
}
for (i in 1:nrow(contrast_ind)){
ind1 <- contrast_ind[i, 1]; ind2 <- contrast_ind[i, 2];
if (i == 1){ # first element
to_track <- data.frame(row.names = c(ind1, ind2), val = c(1, 1))
ans <- matrix(contrast_ind[i, ], nrow = 1)
} else {
if (nrow(ans) == 10) { # want to extract 10 pairs
break
} else {
row_names <- row.names(to_track)
ind1_str <- toString(ind1); ind2_str <- toString(ind2);
if (ind1_str %in% row_names){
first_bool <- to_track[ind1_str, ] < threshold
to_track[ind1_str, ] <- to_track[ind1_str, ] + 1
} else {
to_track[ind1_str, ] <- 1
first_bool <- TRUE
}
if (ind2_str %in% row_names){
second_bool <- to_track[ind2_str, ] < threshold
to_track[ind2_str, ] <- to_track[ind2_str, ] + 1
} else {
to_track[ind2_str, ] <- 1
second_bool <- TRUE
}
if (first_bool & second_bool){
ans <- rbind(ans, contrast_ind[i,])
}
}
}
}
return (ans)
}
2-1-1. Low Pearson (< 10%) and High Spearman (> 95%) (linearity vs monotone)
cor_contrast1 <- ((abs(cor_pearson_mat) < quantile_mat["Pearson", 1]) &
(abs(cor_spearman_mat) > quantile_mat["Spearman", 2]))
cor_contrast_ind1 <- which(cor_contrast1, arr.ind = T)
cor_contrast_ind1 <- contrast_helper(cor_contrast_ind1, 3)
nrow(cor_contrast_ind1)
## [1] 4
2-1-2. Visualization of Low Pearson (< 10%) and High Spearman (> 95%) (linearity vs monotone)
par(mfrow = c(2, 2))
for (i in 1:nrow(cor_contrast_ind1)){
index1 <- cor_contrast_ind1[i, 1]; index2 <- cor_contrast_ind1[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3))))
}
2-2-1. High Pearson (> 95%) and Low Spearman (< 10%) (linearity vs monotone)
cor_contrast2 <- ((abs(cor_pearson_mat) > quantile_mat["Pearson", 2]) &
(abs(cor_spearman_mat) < quantile_mat["Spearman", 1]))
cor_contrast_ind2 <- which(cor_contrast2, arr.ind = T)
cor_contrast_ind2 <- contrast_helper(cor_contrast_ind2, 3)
nrow(cor_contrast_ind2)
## [1] 10
2-2-2. Visualization of High Pearson (> 95%) and Low Spearman (< 10%) (linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind2)){
index1 <- cor_contrast_ind2[i, 1]; index2 <- cor_contrast_ind2[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3))))
}
2-3-1. Low Pearson (< 10%) and High Kendall (> 95%) (linearity vs monotone)
cor_contrast3 <- ((abs(cor_pearson_mat) < quantile_mat["Pearson", 1]) &
(abs(cor_kendall_mat) > quantile_mat["Kendall", 2]))
cor_contrast_ind3 <- which(cor_contrast3, arr.ind = T)
cor_contrast_ind3 <- contrast_helper(cor_contrast_ind3, 3)
nrow(cor_contrast_ind3)
## [1] 5
2-3-2. Visualization of Low Pearson (< 10%) and High Kendall (> 95%) (linearity vs monotone)
par(mfrow = c(2, 3))
for (i in 1:nrow(cor_contrast_ind3)){
index1 <- cor_contrast_ind3[i, 1]; index2 <- cor_contrast_ind3[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Kendall of ", round(cor_kendall_mat[index1, index2], 3))))
}
2-4-1. High Pearson (> 95%) and Low Kendall (< 10%) (linearity vs monotone)
cor_contrast4 <- ((abs(cor_pearson_mat) > quantile_mat["Pearson", 2]) &
(abs(cor_kendall_mat) < quantile_mat["Kendall", 1]))
cor_contrast_ind4 <- which(cor_contrast4, arr.ind = T)
cor_contrast_ind4 <- contrast_helper(cor_contrast_ind4, 3)
nrow(cor_contrast_ind4)
## [1] 10
2-4-2. Visualization of High Pearson (> 95%) and Low Kendall (< 10%) (linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind4)){
index1 <- cor_contrast_ind4[i, 1]; index2 <- cor_contrast_ind4[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Kendall of ", round(cor_kendall_mat[index1, index2], 3))))
}
2-5-1. Low Pearson (< 10%) and High Hoeffding’s D (> 95%) (linearity vs monotone)
cor_contrast5 <- ((abs(cor_pearson_mat) < quantile_mat["Pearson", 1]) &
(abs(cor_hoeffd_mat) > quantile_mat["Hoeffding's D", 2]))
cor_contrast_ind5 <- which(cor_contrast5, arr.ind = T)
cor_contrast_ind5 <- contrast_helper(cor_contrast_ind5, 3)
nrow(cor_contrast_ind5)
## [1] 8
2-5-2. Visualization of Low Pearson (< 10%) and High Hoeffding’s D (> 95%) (linearity vs monotone)
par(mfrow = c(2, 4))
for (i in 1:nrow(cor_contrast_ind5)){
index1 <- cor_contrast_ind5[i, 1]; index2 <- cor_contrast_ind5[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Hoeff D of ", round(cor_hoeffd_mat[index1, index2], 3))))
}
2-6-1. High Pearson (> 95%) and Low Hoeffding’s D (< 10%) (linearity vs monotone)
cor_contrast6 <- ((abs(cor_pearson_mat) > quantile_mat["Pearson", 2]) &
(abs(cor_hoeffd_mat) < quantile_mat["Hoeffding's D", 1]))
cor_contrast_ind6 <- which(cor_contrast6, arr.ind = T)
cor_contrast_ind6 <- contrast_helper(cor_contrast_ind6, 3)
nrow(cor_contrast_ind6)
## [1] 10
2-6-2. Visualization of High Pearson (> 95%) and Low Hoeffding’s D (< 10%) (linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind6)){
index1 <- cor_contrast_ind6[i, 1]; index2 <- cor_contrast_ind6[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Hoeff D of ", round(cor_hoeffd_mat[index1, index2], 3))))
}
2-7-1. Low Pearson (< 10%) and high Blomqvist’s beta (> 95%) (linearity vs monotone)
cor_contrast7 <- ((abs(cor_pearson_mat) < quantile_mat["Pearson", 1]) &
(abs(cor_blomqvist_mat) > quantile_mat["Blomqvist's Beta", 2]))
cor_contrast_ind7 <- which(cor_contrast7, arr.ind = T)
cor_contrast_ind7 <- contrast_helper(cor_contrast_ind7, 3)
nrow(cor_contrast_ind7)
## [1] 0
2-7-2. Visualization of Low Pearson (< 10%) and high Blomqvist’s beta (> 95%) (linearity vs monotone)
# par(mfrow = c(2, 5))
# for (i in 1:nrow(cor_contrast_ind7)){
# index1 <- cor_contrast_ind7[i, 1]; index2 <- cor_contrast_ind7[i, 2]
# plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
# pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
# ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
# main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
# "\n",
# paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
# }
2-8-1. High Pearson (> 95%) and Low Blomqvist’s beta (< 10%) (linearity vs monotone)
cor_contrast8 <- ((abs(cor_pearson_mat) > quantile_mat["Pearson", 2]) &
(abs(cor_blomqvist_mat) < quantile_mat["Blomqvist's Beta", 1]))
cor_contrast_ind8 <- which(cor_contrast8, arr.ind = T)
cor_contrast_ind8 <- contrast_helper(cor_contrast_ind8, 3)
nrow(cor_contrast_ind8)
## [1] 3
2-8-2. Visualization of High Pearson (> 95%) and Low Blomqvist’s beta (< 10%) (linearity vs monotone)
par(mfrow = c(2, 2))
for (i in 1:nrow(cor_contrast_ind8)){
index1 <- cor_contrast_ind8[i, 1]; index2 <- cor_contrast_ind8[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
}
2-11-1. Low Pearson (< 10%) and High XI (> 95%) (linearity vs non-linearity)
cor_contrast11 <- ((abs(cor_pearson_mat) < quantile_mat["Pearson", 1]) &
(abs(cor_XI_mat) > quantile_mat["XI Corr", 2]))
cor_contrast_ind11 <- which(cor_contrast11, arr.ind = T)
cor_contrast_ind11 <- contrast_helper(cor_contrast_ind11, 3)
nrow(cor_contrast_ind11)
## [1] 10
2-11-2. Visualization of Low Pearson (< 10%) and High XI (> 95%) (linearity vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind11)){
index1 <- cor_contrast_ind11[i, 1]; index2 <- cor_contrast_ind11[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("XI Corr of ", round(cor_XI_mat[index1, index2], 3))))
}
2-12-1. High Pearson (> 95%) and Low XI (< 10%) (linearity vs non-linearity)
cor_contrast12 <- ((abs(cor_pearson_mat) > quantile_mat["Pearson", 2]) &
(abs(cor_XI_mat) < quantile_mat["XI Corr", 1]))
cor_contrast_ind12 <- which(cor_contrast12, arr.ind = T)
cor_contrast_ind12 <- contrast_helper(cor_contrast_ind12, 3)
nrow(cor_contrast_ind12)
## [1] 10
2-12-2. Visualization of High Pearson (> 95%) and Low XI (< 10%) (linearity vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind12)){
index1 <- cor_contrast_ind12[i, 1]; index2 <- cor_contrast_ind12[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("XI Corr of ", round(cor_XI_mat[index1, index2], 3))))
}
2-13-1. Low Spearman (< 10%) and High Distance Correlation (> 95%) (monotone vs non-linearity)
cor_contrast13 <- ((abs(cor_spearman_mat) < quantile_mat["Spearman", 1]) &
(abs(cor_dist_mat) > quantile_mat["Dist. Corr", 2]))
cor_contrast_ind13 <- which(cor_contrast13, arr.ind = T)
cor_contrast_ind13 <- contrast_helper(cor_contrast_ind13, 3)
nrow(cor_contrast_ind13)
## [1] 10
2-13-2. Visualization of Low Spearman (< 10%) and High Distance Correlation (> 95%) (monotone vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind13)){
index1 <- cor_contrast_ind13[i, 1]; index2 <- cor_contrast_ind13[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
"\n",
paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3))))
}
2-14-1. High Spearman (> 95%) and Low Distance Correlation (< 10%) (monotone vs non-linearity)
cor_contrast14 <- ((abs(cor_spearman_mat) > quantile_mat["Spearman", 2]) &
(abs(cor_dist_mat) < quantile_mat["Dist. Corr", 1]))
cor_contrast_ind14 <- which(cor_contrast14, arr.ind = T)
cor_contrast_ind14 <- contrast_helper(cor_contrast_ind14, 3)
nrow(cor_contrast_ind14)
## [1] 10
2-14-2. Visualization of High Spearman (> 95%) and Low Distance Correlation (< 10%) (monotone vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind14)){
index1 <- cor_contrast_ind14[i, 1]; index2 <- cor_contrast_ind14[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
"\n",
paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3))))
}
2-15-1. Low Spearman (< 10%) and High Blomqvist’s Beta (> 95%) (monotone vs monotone)
cor_contrast15 <- ((abs(cor_spearman_mat) < quantile_mat["Spearman", 1]) &
(abs(cor_blomqvist_mat) > quantile_mat["Blomqvist's Beta", 2]))
cor_contrast_ind15 <- which(cor_contrast15, arr.ind = T)
cor_contrast_ind15 <- contrast_helper(cor_contrast_ind15, 3)
nrow(cor_contrast_ind15)
## [1] 0
2-15-2. Visualization of Low Spearman (< 10%) and High Blomqvist’s Beta (> 95%) (monotone vs monotone)
# par(mfrow = c(2, 5))
# for (i in 1:nrow(cor_contrast_ind15)){
# index1 <- cor_contrast_ind15[i, 1]; index2 <- cor_contrast_ind15[i, 2]
# plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
# pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
# ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
# main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
# "\n",
# paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
# }
2-16-1. High Spearman (> 95%) and Low Blomqvist’s Beta (< 10%) (monotone vs monotone)
cor_contrast16 <- ((abs(cor_spearman_mat) > quantile_mat["Spearman", 2]) &
(abs(cor_blomqvist_mat) < quantile_mat["Blomqvist's Beta", 1]))
cor_contrast_ind16 <- which(cor_contrast16, arr.ind = T)
cor_contrast_ind16 <- contrast_helper(cor_contrast_ind16, 3)
nrow(cor_contrast_ind16)
## [1] 7
2-16-2. Visualization of High Spearman (> 95%) and Low Blomqvist’s Beta (< 10%) (monotone vs monotone)
par(mfrow = c(2, 4))
for (i in 1:nrow(cor_contrast_ind16)){
index1 <- cor_contrast_ind16[i, 1]; index2 <- cor_contrast_ind16[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
"\n",
paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
}
2-17-1. Low Spearman (< 10%) and High Hoeffding’s D (> 95%) (monotone vs monotone)
cor_contrast17 <- ((abs(cor_spearman_mat) < quantile_mat["Spearman", 1]) &
(abs(cor_blomqvist_mat) > quantile_mat["Hoeffding's D", 2]))
cor_contrast_ind17 <- which(cor_contrast17, arr.ind = T)
cor_contrast_ind17 <- contrast_helper(cor_contrast_ind17, 3)
nrow(cor_contrast_ind17)
## [1] 10
2-17-2. Visualization of Low Spearman (< 10%) and High Hoeffding’s D (> 95%) (monotone vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind17)){
index1 <- cor_contrast_ind17[i, 1]; index2 <- cor_contrast_ind17[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
"\n",
paste0("Hoeff D of ", round(cor_hoeffd_mat[index1, index2], 3))))
}
2-18-1. High Spearman (> 95%) and Low Hoeffding’s D (< 10%) (monotone vs monotone)
cor_contrast18 <- ((abs(cor_spearman_mat) > quantile_mat["Spearman", 2]) &
(abs(cor_blomqvist_mat) < quantile_mat["Hoeffding's D", 1]))
cor_contrast_ind18 <- which(cor_contrast18, arr.ind = T)
cor_contrast_ind18 <- contrast_helper(cor_contrast_ind18, 3)
nrow(cor_contrast_ind18)
## [1] 0
2-18-2. Visualization of High Spearman (> 95%) and Low Hoeffding’s D (< 10%) (monotone vs monotone)
# par(mfrow = c(2, 5))
# for (i in 1:nrow(cor_contrast_ind18)){
# index1 <- cor_contrast_ind18[i, 1]; index2 <- cor_contrast_ind18[i, 2]
# plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
# pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
# ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
# main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
# "\n",
# paste0("Hoeff D of ", round(cor_hoeffd_mat[index1, index2], 3))))
# }
2-21-1. Low Spearman (< 10%) and High XI (> 95%) (monotone vs non-linearity)
cor_contrast21 <- ((abs(cor_spearman_mat) < quantile_mat["Spearman", 1]) &
(abs(cor_XI_mat) > quantile_mat["XI Corr", 2]))
cor_contrast_ind21 <- which(cor_contrast21, arr.ind = T)
cor_contrast_ind21 <- contrast_helper(cor_contrast_ind21, 3)
nrow(cor_contrast_ind21)
## [1] 10
2-21-2. Visualization of Low Spearman (< 10%) and High XI (> 95%) (monotone vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind21)){
index1 <- cor_contrast_ind21[i, 1]; index2 <- cor_contrast_ind21[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
"\n",
paste0("XI of ", round(cor_XI_mat[index1, index2], 3))))
}
2-22-1. High Spearman (> 95%) and Low XI (< 10%) (monotone vs non-linearity)
cor_contrast22 <- ((abs(cor_spearman_mat) > quantile_mat["Spearman", 2]) &
(abs(cor_XI_mat) < quantile_mat["XI Corr", 1]))
cor_contrast_ind22 <- which(cor_contrast22, arr.ind = T)
cor_contrast_ind22 <- contrast_helper(cor_contrast_ind22, 3)
nrow(cor_contrast_ind22)
## [1] 10
2-22-2. Visualization of High Spearman (> 95%) and Low XI (< 10%) (monotone vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind22)){
index1 <- cor_contrast_ind22[i, 1]; index2 <- cor_contrast_ind22[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3)),
"\n",
paste0("XI Corr of ", round(cor_XI_mat[index1, index2], 3))))
}
2-23-1. Low Distance Correlation (< 10%) and High Hoeffiding’s D (> 95%) (non-linearity vs monotone)
cor_contrast23 <- ((abs(cor_dist_mat) < quantile_mat["Dist. Corr", 1]) &
(abs(cor_hoeffd_mat) > quantile_mat["Hoeffding's D", 2]))
cor_contrast_ind23 <- which(cor_contrast23, arr.ind = T)
cor_contrast_ind23 <- contrast_helper(cor_contrast_ind23, 3)
nrow(cor_contrast_ind23)
## [1] 10
2-23-2. Visualization of Low Distance Correlation (< 10%) and High Hoeffiding’s D (> 95%) (non-linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind23)){
index1 <- cor_contrast_ind23[i, 1]; index2 <- cor_contrast_ind23[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3)),
"\n",
paste0("Hoeffiding's D of ", round(cor_hoeffd_mat[index1, index2], 3))))
}
2-24-1. High Distance Correlation (> 95%) and Low Hoeffiding’s D (< 10%) (non-linearity vs monotone)
cor_contrast24 <- ((abs(cor_dist_mat) > quantile_mat["Dist. Corr", 2]) &
(abs(cor_hoeffd_mat) < quantile_mat["Hoeffding's D", 1]))
cor_contrast_ind24 <- which(cor_contrast24, arr.ind = T)
cor_contrast_ind24 <- contrast_helper(cor_contrast_ind24, 3)
nrow(cor_contrast_ind24)
## [1] 10
2-24-2. Visualization of High Distance Correlation (> 95%) and Low Hoeffiding’s D (< 10%) (non-linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind24)){
index1 <- cor_contrast_ind24[i, 1]; index2 <- cor_contrast_ind24[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3)),
"\n",
paste0("Hoeffiding's D of ", round(cor_hoeffd_mat[index1, index2], 3))))
}
2-25-1. Low Distance Correlation (< 10%) and High XI (> 95%) (non-linearity vs non-linearity)
cor_contrast25 <- ((abs(cor_dist_mat) < quantile_mat["Dist. Corr", 1]) &
(abs(cor_XI_mat) > quantile_mat["XI Corr", 2]))
cor_contrast_ind25 <- which(cor_contrast25, arr.ind = T)
cor_contrast_ind25 <- contrast_helper(cor_contrast_ind25, 3)
nrow(cor_contrast_ind25)
## [1] 10
2-25-2. Visualization of Low Distance Correlation (< 10%) and High XI (> 95%) (non-linearity vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind25)){
index1 <- cor_contrast_ind25[i, 1]; index2 <- cor_contrast_ind25[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3)),
"\n",
paste0("XI Corr of ", round(cor_XI_mat[index1, index2], 3))))
}
2-26-1. High Distance Correlation (> 95%) and Low XI (< 10%) (non-linearity vs non-linearity)
cor_contrast26 <- ((abs(cor_dist_mat) > quantile_mat["Dist. Corr", 2]) &
(abs(cor_XI_mat) < quantile_mat["XI Corr", 1]))
cor_contrast_ind26 <- which(cor_contrast26, arr.ind = T)
cor_contrast_ind26 <- contrast_helper(cor_contrast_ind26, 3)
nrow(cor_contrast_ind26)
## [1] 10
2-26-2. Visualization of High Distance Correlation (> 95%) and Low XI (< 10%) (non-linearity vs non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind26)){
index1 <- cor_contrast_ind26[i, 1]; index2 <- cor_contrast_ind26[i, 2]
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = paste(paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3)),
"\n",
paste0("XI of ", round(cor_XI_mat[index1, index2], 3))))
}
2-27-1. Low Distance Correlation (< 10%) and High Blomqvist’s Beta (> 95%) (non-linearity vs non-linearity)
cor_contrast27 <- ((abs(cor_dist_mat) < quantile_mat["Dist. Corr", 1]) &
(abs(cor_blomqvist_mat) > quantile_mat["Blomqvist's Beta", 2]))
cor_contrast_ind27 <- which(cor_contrast27, arr.ind = T)
cor_contrast_ind27 <- contrast_helper(cor_contrast_ind27, 3)
nrow(cor_contrast_ind27)
## [1] 0
2-27-2. Visualization of Low Distance Correlation (< 10%) and High Blomqvist’s Beta (> 95%) (non-linearity vs non-linearity)
# par(mfrow = c(2, 5))
# for (i in 1:nrow(cor_contrast_ind27)){
# index1 <- cor_contrast_ind27[i, 1]; index2 <- cor_contrast_ind27[i, 2]
# plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
# pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
# ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
# main = paste(paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3)),
# "\n",
# paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
# }
2-28-1. High Distance Correlation (> 95%) and Low Blomqvist’s Beta (< 10%) (non-linearity vs non-linearity)
cor_contrast28 <- ((abs(cor_dist_mat) > quantile_mat["Dist. Corr", 2]) &
(abs(cor_blomqvist_mat) < quantile_mat["Blomqvist's Beta", 1]))
cor_contrast_ind28 <- which(cor_contrast28, arr.ind = T)
cor_contrast_ind28 <- contrast_helper(cor_contrast_ind28, 3)
nrow(cor_contrast_ind28)
## [1] 0
2-28-2. Visualization of High Distance Correlation (> 95%) and Low Blomqvist’s Beta (< 10%) (non-linearity vs non-linearity)
# par(mfrow = c(2, 5))
# for (i in 1:nrow(cor_contrast_ind28)){
# index1 <- cor_contrast_ind28[i, 1]; index2 <- cor_contrast_ind28[i, 2]
# plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
# pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
# ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
# main = paste(paste0("Dist. Cor of ", round(cor_dist_mat[index1, index2], 3)),
# "\n",
# paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
# }
3. Explore dense plots
3-1. Visualize dense plot
dense_ind <- rbind(c(50, 10), c(66, 53), c(473, 400), c(389, 1),
c(397, 147), c(133, 106), c(30, 28))
dense_title <-
c(paste(paste0("Pearson of ", round(cor_pearson_mat[dense_ind[1,1], dense_ind[1,2]], 3),
" XI of ", round(cor_XI_mat[dense_ind[1,1], dense_ind[1,2]], 3)),
"\n",
paste0("Kendall of ", round(cor_kendall_mat[dense_ind[1,1], dense_ind[1,2]], 3),
" Dist Cor. of ", round(cor_dist_mat[dense_ind[1,1], dense_ind[1,2]], 3))),
paste(paste0("Pearson of ", round(cor_pearson_mat[dense_ind[2,1], dense_ind[2,2]], 3),
" XI of ", round(cor_XI_mat[dense_ind[2,1], dense_ind[2,2]], 3)),
"\n",
paste0("Kendall of ", round(cor_kendall_mat[dense_ind[2,1], dense_ind[2,2]], 3),
" Dist Cor. of ", round(cor_dist_mat[dense_ind[2,1], dense_ind[2,2]], 3))),
paste(paste0("XI of ", round(cor_XI_mat[dense_ind[3,1], dense_ind[3,2]], 3)),
"\n",
paste0("Pearson of ", round(cor_pearson_mat[dense_ind[3,1], dense_ind[3,2]], 3),
" Dist Cor of ", round(cor_dist_mat[dense_ind[3,1], dense_ind[3,2]], 3))),
paste(paste0("XI of ", round(cor_XI_mat[dense_ind[4,1], dense_ind[4,2]], 3)),
" NMI of ", round(cor_MI_mat[dense_ind[4,1], dense_ind[4,2]], 3),
"\n",
paste0("Hoeff D of ", round(cor_hoeffd_mat[dense_ind[4,1], dense_ind[4,2]], 3))),
paste(paste0("XI of ", round(cor_XI_mat[dense_ind[5,1], dense_ind[5,2]], 3)),
"\n",
paste0("NMI of ", round(cor_MI_mat[dense_ind[5,1], dense_ind[5,2]], 3),
" Dist Cor of ", round(cor_dist_mat[dense_ind[5,1], dense_ind[5,2]], 3))),
paste(paste0("XI of ", round(cor_XI_mat[dense_ind[6,1], dense_ind[6,2]], 3)),
"\n",
paste0("NMI of ", round(cor_MI_mat[dense_ind[6,1], dense_ind[6,2]], 3),
" Hoeff D of ", round(cor_hoeffd_mat[dense_ind[6,1], dense_ind[6,2]], 3))),
paste(paste0("XI of ", round(cor_XI_mat[dense_ind[7,1], dense_ind[7,2]], 3)),
"\n",
paste0("Hoeff D of ", round(cor_hoeffd_mat[dense_ind[7,1], dense_ind[7,2]], 3),
" NMI of ", round(cor_MI_mat[dense_ind[7,1], dense_ind[7,2]], 3))))
index1 <- dense_ind[1, 1]; index2 <- dense_ind[1, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[1]
)
- The plot depicts a vertical line above, having a relatively high XI and Pearson correlation. As the pattern is vertical, it is hard to have a monotonic relationship of X and Y that it has low kendall coefficient. Also, it is not dense, so it would have low distance correlation.
index1 <- dense_ind[2, 1]; index2 <- dense_ind[2, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[2]
)
- It is interesting to see that the plot shows a dense cluster on the middle bottom. However, it has lower distance correlation and high pearson correlation.
index1 <- dense_ind[3, 1]; index2 <- dense_ind[3, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[3]
)
- As the points are stretched along the horizontal line, it has a very low pearson correlation and distance correlation.
index1 <- dense_ind[4, 1]; index2 <- dense_ind[4, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[4]
)
- It shows a vertical line that the pattern has high XI and NMI correlation. It is interesting to see that NMI is high; it is unsure, but it might be most of the points are around SERF2 = 0 and \(\text{TMSB4X} < 500\)
index1 <- dense_ind[5, 1]; index2 <- dense_ind[5, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[5]
)
- The plot above illustrates that the points are scattered horizontally. It is worth noting that all the plots have higher values of XI.
index1 <- dense_ind[6, 1]; index2 <- dense_ind[6, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[6]
)
index1 <- dense_ind[7, 1]; index2 <- dense_ind[7, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[7]
)
- It is interesting to see that the scattere points without forming a certain pattern have a high value of XI for plot 6 and plot 7.
3-2. Visualize with alpha parameter (transparency)
par(mfrow = c(2, 2))
for (i in 1:nrow(dense_ind)){
index1 <- dense_ind[i, 1]; index2 <- dense_ind[i, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = scales::alpha(sub_cluster_labels, 0.2), asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[i])
}
3-3. Visualize with contour plots (density)
#' Plotting density
#'
#' @param mat matrix
#' @param grid_spacing numeric vector
#' @param n integer for \code{stats::kde}
#' @param max_num integer
#' @param density_colors color vector
#' @param point_color color
#' @param contour_color color
#' @param grid_color color
#' @param pch integer
#' @param contour_lwd numeric
#' @param grid_lty integer
#' @param grid_lwd numeric
#' @param ... additional graphical parameters
#'
#' @return nothing
#' @export
plot_density <- function(mat, grid_spacing,
xlim,
ylim,
n = 100,
max_num = 20000,
density_colors = grDevices::heat.colors(100, alpha = 0.8),
point_color = grDevices::rgb(0.5, 0.5, 0.5, 0.8),
contour_color = grDevices::rgb(1,1,1,0.5),
grid_color = "gray",
xaxt = "n",
yaxt = "n",
axes = F,
xlab = "",
ylab = "",
pch = 16,
contour_lwd = 2,
grid_lty = 2,
grid_lwd = 0.5,
...){
stopifnot(ncol(mat) == 2)
mat2 <- rbind(mat,
c(xlim[1], ylim[1]),
c(xlim[1], ylim[2]),
c(xlim[2], ylim[1]),
c(xlim[2], ylim[2]))
f1 <- MASS::kde2d(mat2[,1], mat2[,2], n = 100)
graphics::image(f1,
col = density_colors,
xlim = xlim,
ylim = ylim,
...)
for(i in grid_spacing){
graphics::lines(rep(i,2), c(-2,2)*max(abs(grid_spacing)),
lty = grid_lty,
lwd = grid_lwd,
col = grid_color)
graphics::lines(c(-2,2)*max(abs(grid_spacing)), rep(i,2),
lty = grid_lty,
lwd = grid_lwd,
col = grid_color)
}
if(nrow(mat) > max_num) {
idx <- sample(1:nrow(mat), size = max_num)
} else {
idx <- 1:nrow(mat)
}
graphics::points(mat[idx,1], mat[idx,2],
col = point_color,
pch = pch)
graphics::contour(f1, add = T,
drawlabels = F,
col = contour_color,
lwd = contour_lwd)
invisible()
}
par(mfrow = c(1, 2))
for (i in 1:nrow(dense_ind)){
index1 <- dense_ind[i, 1]; index2 <- dense_ind[i, 2];
plot(saver_mat[,index1], saver_mat[,index2], col = sub_cluster_labels, asp = T,
pch = 16, xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"),
main = dense_title[i])
xylim <- par("usr")
x <- saver_mat[,index1]; y <- saver_mat[,index2];
xmin <- min(x); xmax <- max(x); ymin <- min(y); ymax <- max(y);
total_min <- min(xmin, ymin); total_max <- max(xmax, ymax);
plot_density(cbind(x, y),
grid_spacing = seq(total_min, total_max, by=((total_max - total_min) / 10)),
xlim = c(xylim[1], xylim[2]), ylim = c(xylim[3], xylim[4]),
xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"))
}
3-4 Visualize with HexBin
library(hexbin)
library(RColorBrewer)
par(mfrow = c(2,3))
for (i in 1:nrow(dense_ind)){
index1 <- dense_ind[i, 1]; index2 <- dense_ind[i, 2];
bin <- hexbin(saver_mat[,index1], saver_mat[,index2], xbins = 40)
my_colors=colorRampPalette(rev(brewer.pal(11, 'Spectral')))
plot(bin, colramp = my_colors, legend = F,
xlab = paste0(colnames(saver_mat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(saver_mat)[index2], ", (", index2, ")"))
}
